arXiv Open Access 2026

Purely cosmetic surgeries and Casson--Walker--Lescop invariants

Kazuhiro Ichihara In Dae Jong Yasuyoshi Tsutsumi

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Abstrak

Using the rational surgery formula for the Casson--Walker--Lescop invariant of links in the $3$-sphere, we show that any null-homologous knot in a rational homology sphere admits at most two pairs of integral purely cosmetic surgeries. We also present constraints for null-homologous knots in certain $3$-manifolds with the first Betti number one or two to admit purely cosmetic surgeries. As another application, we show that, for a null-homologous knot in some $3$-manifolds, including $S^2 \times S^1$, there are at most two knots which are inequivalent to the given one, but whose exteriors are orientation-preservingly homeomorphic to that of the given one.

Topik & Kata Kunci

math.GT

Penulis (3)

Kazuhiro Ichihara

In Dae Jong

Yasuyoshi Tsutsumi

Format Sitasi

APA MLA BibTeX

Ichihara, K., Jong, I.D., Tsutsumi, Y. (2026). Purely cosmetic surgeries and Casson--Walker--Lescop invariants. https://arxiv.org/abs/2603.11720

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2026
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓